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Module #27Module #27
Composite Materials(an overview)
READING LIST►DIETER: Ch. 6, Pages 220-226.
• Chapter 15 in Meyers & Chawla.• N. Chawla & K.K. Chawla, Metal Matrix Composites, Springer
(2006)• D. Hull & T.W. Clyne, An Introduction to Composite Materials, 2nd
Edition, Cambridge (1996)
IntroductionIntroduction
• So far, we’ve considered the improvement of the mechanical properties of materials by modifying the internal structure of the material system either by alloying or processing.
• We can also develop materials with even different properties by introducing additional phases/materials into a host material. This mixture of phases is termed a composite.
• In general, composites are relatively macroscopic mixtures of phases/materials. These mixtures are sometimes natural, but are generally artificial.
• By mixing two different phases or materials, we can develop materials that have properties which are an average of those of the two components.
Introduction (2)Introduction (2)• In a composites, strength/properties = average of
strength/properties of the individual materials.
• We design composites so as to obtain the best attributes of the individual constituents.
• Microstructure of a composite = matrix + reinforcement
– Matrix: • phase that holds reinforcement together• protects the reinforcement• transmits load to the reinforcement.
– Reinforcement: • filaments, fibers, whiskers, etc., which have intrinsically high strength and modulus;
reinforcements are often too brittle to use in monolithic forms. Sometimes “soft” reinforcements are used too.
Introduction (3)Introduction (3)• Interface between reinforcement and matrix is often the most
critical element in determining materials properties and performance.
– Is interface strong or weak?
• Influences transfer of stress from matrix to fiber
• Influences crack propagation
• Etc.
– Is there reaction at the interface? Is there no reaction?
• Reactions change the properties of the fiber and matrix locally. Chemistry change
• Stress concentration
• Etc.
Classification of Composites (1)Classification of Composites (1)
• On basis of matrix:
– Polymer matrix composites (PMCs)
– Metal matrix composites (MMCs)
– Ceramic matrix composites (CMCs)
• Purpose of reinforcement
– PMC: increase stiffness (E), yield strength, tensile strength, and creep resistance
– MMC: increase yield strength, tensile strength, and creep resistance
– CMC: increase fracture toughness (Kc)
Classification of Composites (2)Classification of Composites (2)
• On basis of reinforcement
– Particle reinforced composites• Natural
– Ex., precipitates• Artificial
– Addition of immiscible phases
– Short fiber or whisker reinforced composites• Artificial
– Continuous fiber or sheet reinforced MMCs• Natural (“sort of”)
– Ex., DS eutectics• Artificial
[Meyers & Chawla]
What can composites look like?What can composites look like?
Fiber reinforced
[Meyers & Chawla]
MMC
Figure 15.1 (a) Transverse section of a boron fiber reinforced aluminum composite. Vf = 10%. (b) Transverse section of a carbon fiber reinforced polyester resin. Vf = 50% (Optical). (c) Deeply etched transverse section of a eutectic composite showing NbC fibers in a Ni-Cr matrix. (d) SiC particles in an Al alloy matrix (SEM). Vf = 17%.
Particle reinforced
Fiber reinforced
Fiber reinforced (eutectic)
PMC
MMC MMC
(a) (b)
(c) (d)[Meyers & Chawla]
What can composites look like?What can composites look like?
Which phase is the reinforcing phase?
MMC
[Bewlay et al., MRS Bulletin, v.28, n.9 (2003) p. 646-653]
Figure 5. Microstructural evolution in Nb-19.5Ti-13Cr-2Hf-17.5Si-2Al-1.2Sn (at.%) in the following conditions: (a) as-cast, (b) homogenized (1300°C/24h + 1400°C/76 h), and (c), (d) extruded (1350°C at 6:1 ratio), transverse and longitudinal sections, respectively. The light phase is Nb, the gray phase in (Nb)5Si3, and the black phase is the Cr2(Nb)-type Laves phase.
(a) (b)
(a) (b)
GRAY DUCTILE
WHITE MALLEABLE
graphite
-ferrite
Fe3C
pearlite
graphite
-ferrite
graphite
-ferrite
[From Callister, 7th Ed., Fig. 11.3, pages 367-368]
Cast Iron: another good example of a compositeCast Iron: another good example of a compositeParticle reinforced MMCs
What do properties depend upon?What do properties depend upon?
• Matrix type– Structure and intrinsic properties
• Reinforcement:– Concentration– Shape– Size– Distribution– Orientation– Matrix/reinforcement interface
• To begin, we will consider a laminate composite in order to develop the basic principles of reinforcement.
Basic mechanics (1)Basic mechanics (1)
• Consider the case where a force is applied along the y-direction. In this instance, the stresses on the and lamellae are equal (i.e., = F/L2).
• The composite strain is the weighted average of the individual strains in each lamellae.
• The composite modulus is given by:
x
y
z
L L
L
L( )
( )
LVL L
LV
L L
c V V
N(L + L)
c
E EE
V E V E
Force
Let be the strong phase
Does Does strengthstrength change as we alter volume change as we alter volume fraction of reinforcing phase?fraction of reinforcing phase?
Answer: NOT FOR THIS ARRANGEMENT!
0 1
1
FF
V
With this type of loading, both phases experience the same force and thus the same stress. Therefore, F/F = 1.
Let F = strong phase.
The force ratio is independent of V.
• Point 1:– V = 0.5; V = 0.5– E = 100 GPa; E = 10 GPa
21000
100055
GPa(0.5 10 GPa + 0.5 100 GPa)
GPa = 18.1 GPa
cE
• Point 2:– V = 0.1; V = 0.9– E = 100 GPa; E = 10 GPa
21000
100091
GPa(0.1 10 GPa + 0.9 100 GPa)
GPa = 11 GPa
cE
• Point 3:– V = 0.9; V = 0.1– E = 100 GPa; E = 10 GPa
21000
100019
GPa(0.9 10 GPa + 0.1 100 GPa)
GPa = 52.6 GPa
cE
0.0 0.2 0.4 0.6 0.8 1.00
20
40
60
80
100
Com
posi
te M
odul
us (G
Pa)
Volume Fraction of -phase
#1#2
#3
Does Does modulusmodulus change as we alter volume change as we alter volume fraction of reinforcing phase?fraction of reinforcing phase?
Answer: YES!
Equal stress condition
Basic mechanics (2)Basic mechanics (2)
• Consider the case where a force is applied along the z-direction. In this instance, the stresses on the and lamellae are different.
• The strains on the and lamellae are equal.
• The composite modulus is given by:
x
y
z
L L
L
L( )
( )
LVL L
LV
L L
c
N(L + L)
cE V E V E
Forc
e
Once again, let be the strong phase
0.0 0.2 0.4 0.6 0.8 1.00
20
40
60
80
100
Com
posi
te M
odul
us (G
Pa)
Volume Fraction of -phase
• Point 1:– V = 0.5; V = 0.5– E = 100 GPa; E = 10 GPa
55(0.5 100 GPa + 0.5 10 GPa)
GPacE
• Point 2:– V = 0.1; V = 0.9– E = 100 GPa; E = 10 GPa
19(0.1 100 GPa + 0.9 10 GPa)
GPacE
• Point 3:– V = 0.9; V = 0.1– E = 100 GPa; E = 10 GPa
91(0.9 100 GPa + 0.1 10 GPa)
GPacE
Does Does modulusmodulus change as we alter volume change as we alter volume fraction of reinforcing phase?fraction of reinforcing phase?
Answer: YES!
Equal strain condition
0.0 0.2 0.4 0.6 0.8 1.00
20
40
60
80
100
Com
posi
te M
odul
us (G
Pa)
Volume Fraction of -phase
This is a composite plot of the elastic modulus for the composite that we used in the example. The blue curve shows the upper bound for modulus and the red curve shows the lower bound as calculated using the rule of mixtures. The moduli of particle-reinforced materials generally lies between the values predicted for laminate composites, but near the lower bound. In fact, for particle reinforced composites:
c
E EE
V E V E
cE V E V E
,
)
c m m c p p c m m s p p
c s
c s
E V E K V E V K V
K KK K
and
where and are empirical constants with values of less than 1(
Equal strain condition
Equal stress condition
E = 100 GPa E = 10 GPa
More effective use of stiffness of the α phase
Basic mechanics (3)Basic mechanics (3)
• The composite stress for this arrangement is given by:
x
y
z
L L
L
L
N(L + L)
c V V
Forc
eOnce again, let be
the strong phase
• What this plot shows is that the equal-strain condition for reinforcement (i.e., strong phase aligned parallel to applied force) is most useful for reinforcement.
• Under these conditions, the strengthening phase (i.e., the reinforcement) is much more effective at carrying load.
• However, there must be a certain volume fraction of the reinforcing phase present.
Increasing reinforcement strength/stiffness
Equal-stress arrangement
Influence of reinforcement arrangement on strengthInfluence of reinforcement arrangement on strength
[after Courtney, p. 251]
0
2
4
6
8
10
0 0.2 0.4 0.6 1.00.8
Equal-strain arrangement
E α/Eβ
=1
E α/Eβ
=2
E α/Eβ
=5
E α/Eβ
=10
F α/Fβ
Vα
Fα/Fβ = 1
More effective use of stiffness of the α phase
Reinforcement with continuous fibers (1)Reinforcement with continuous fibers (1)
• Most widely utilized phase geometry.
• WHY? Extraordinary strengths can be obtained in fibrous materials. Some particularly important ones are noted in this table.
• High strength fibers must be protected as their fracture toughness is generally low.
[Courtney]
Reinforcement with continuous fibers (2)Reinforcement with continuous fibers (2)
matrix
fibers
c f f m mV V
c
c
I
IIIII “Stress-strain
behavior is a composite too”
f
c
c
I
IIIII
• Stage I– Both fiber and matrix deform elastically.
• Stage II– Generally, the matrix will begin to deform plastically at a strain that
is less than the elastic limit of the fiber.
c c c c f f m mE V E V E
c
stress carriedby matrix atstrain
c f c f c m fV E V
f
c
c
I
IIIII
f
• Stage III– This stage only occurs if the fibers deform plastically prior to
fracture
• f = fiber failure strain– Fibers begin to deform locally or fracture.
c f f c m m cV V
UTS of matrix
Matrix fracture
Fiber fracture
Critical fiber volume fraction needed to strengthenCritical fiber volume fraction needed to strengthen
• Vc = critical volume fraction of fibers
• Vmin = minimum fiber volume fraction required to increase strength of matrix
m
Fiber volume fraction, Vf
Stre
ss
0 1
f
Vc
Vmin
( )c f f m m fV V
(1 )c m m f mV V
min
( )( )
m m f
f m f
V
( )( )
m m fc
f m m f
V
Typical values for Vc and Vminrange from 0.02 to 0.10
Discontinuous fibersDiscontinuous fibers• The equal strain volume fraction rule does not apply to composites
containing discontinuous fibers.
• In discontinuous fibers, there is a critical fiber length Lc for effective strengthening.
where f = tensile strength of fiber, m = shear strength of fiber-matrix interface, and d = fiber diameter.
• For glass and carbon composites, Lc (20 – 150 d) mm.
• Fibers that are shorter than the critical length have less strengthening per unit volume than continuous fibers.
• WHY?
fc
m
dL
Figure 6.9 (a) A schematic of a matrix containing discontinuous fibers. (b) The geometry of one fiber is shown in the cross-hatched region. At the fiber end, tensile load can’t be instantaneously transferred to the fiber from the matrix. (c) The tensile load-transfer process is accomplished by development of a shear stress at the fiber-matrix interface owing to the relative displacement of the fiber and matrix along this interface. The displacement is proportional to the arrows shown, and is zero at the fiber midpoint and a maximum at the fiber end. (d) A small increment of length dx of a fiber; the incremental fiber tensile stress (dσf) is obtained by a force balance; i.e., (πdf2/4) df = m(πdf2dx), where m is the interfacial shear stress.
[after Courtney, p. 258]
Fiber midpoint
Fiber midpoint
Fiber
dx
MatrixF
(a) (b)
(c) (d)
dx
f
m
• The shear stress at the midpoint of a fiber is less than that atthe ends.
• Fibers do work by transferring load from the “weak” matrix to the “strong/stiff” fiber. This requires a large interfacial area.
[after Courtney, p. 259]
matrixfiber
• No load is transferred to the fiber at its ends.
• Load is transferred along the length of the fiber
[after Courtney, p. 259]
• Fibers need to be of a certain length to yield maximum strengthening.
• Read the captions for the two figures presented on the left.
• Fiber orientation is also important.
F
fibers
Fcos
[Courtney]
Fiber failure
Shear yielding of matrix
Normal yielding of matrix
4 4
2 2, 2 2 2 2* * *
cos 1 1 sincos sinUTS c
my
Tsai-Hill failure criterion for fiber reinforce composites
[Courtney]
CrossCross--PlyingPlying• Cross-plying aligned fibers to
produce sandwich structures provides better utilization of composites.
• A 0-90° composite is illustrated to the right.
• Most composites contain more than two plies.
• Other ply arrangements are possible and are used to improve in-plane loading.
Schematic of a 0-90° cross-ply fiber composite. Such configurations are useful for biaxial loading of composites. Other configurations (e.g. 0-45°, 45-45°, or 0-45-90°) can be similarly employed. [Figure scanned from Courtney, p. 267].
